6. How do you, when writing dialogue, make sure that each character sounds like a unique person?
Start with distinct, unique characters.
One thing I'm probably going to end up saying over and over during the course of this series is that conflict = drama. My suspicion is that if you're getting the critique that your characters all sound the same it's because they're difficult to tell apart for other reasons as well. They all come from the same socio-economic class. They're all the same ethnicity/race/(or in the case of science fiction/urban fantasy) species. They have the same agenda/goals. In other words, they have too much in common.
Romances are rarely exciting (to me, at least,) if a lady is marrying a lord she's perfectly suitable for. Better, IMHO, that she's totally smitten by the gardener/slave-gladiator/space pirate/rogue, etc. who is not only so WRONG for her (on the surface, of course), but completely outside of her expected socio-economic pairing.
If you've got a high class princess and a slave-gladiator in the same room talking to each other and they sound the same, then, I'm sorry to say: you're just not thinking.
The slave-gladiator isn't going to use fifteen dollar words, because he likely wasn't educated (if he was, your princess ought to be shocked and there better be a fascinating reason for it). Even if he was once a great lord/general/etc., his life now will probably be rougher and his language ought to show it. More swear words (or their equivalent). Less philosophical debate, more show me the money, as it were.
And, honestly, that's one of the easiest "tricks" (if you really need one). Make your heroine a space commander who uses crisp, militaristic sparse sentences. "Come. Now."
Meanwhile, your hero is a total fop of a space pirate that he uses twenty, lovely poetic words when he could use two. "Darling, only if you press those pert lips against my lily white a$$."
If you really KNOW your characters and their background this won't be difficult. Even if by some accident of plot you have two people (or more) together who are all from the exact same place and time, as long as they all have different agendas they will "sound" different because the reader will know who is who by who wants what.